Computational materials science

Which statement about the interatomic potentials used in molecular dynamics is correct?

  1. AThe Lennard-Jones potential is a pair potential depending only on the distance between two atoms, and it also describes metallic bonding and the directionality of covalent bonds well
  2. BThe embedded atom method (EAM) potential adds an embedding energy that depends on the electron density created by the surrounding atoms, describing the many-body nature of metallic bonding
  3. CFor covalent crystals such as silicon, a pair potential that does not depend on bond angles is the most suitable
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Answer: B. The embedded atom method (EAM) potential adds an embedding energy that depends on the electron density created by the surrounding atoms, describing the many-body nature of metallic bonding

The Lennard-Jones potential is a pair potential depending only on the distance between two atoms; it describes weak, non-directional bonding such as that of the noble gases well, but not the properties of metals or covalent bonds. In metals, the many-body effect, in which the bond strength of an atom changes with the number of surrounding atoms, is large, and EAM adds this as a function of the electron density created by the surrounding atoms. With pair potentials alone, the Cauchy relation C₁₂ = C₄₄ between the elastic constants always holds for an unstressed FCC or BCC crystal, in which every atom sits at a center of symmetry, but many metals do not satisfy it. In covalent bonding the bond angle matters, so the Stillinger–Weber and Tersoff potentials, which include angular terms, are used. Machine-learning potentials trained on DFT results are also widely used.

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More Computational materials science questions

  1. Argon is described by the Lennard-Jones potential V(r) = 4ε[(σ/r)¹² − (σ/r)⁶] with σ = 0.34 nm. Which is closest to the interatomic distance r₀ at which the energy is a minimum?
  2. In a molecular dynamics calculation of a monatomic system, the average kinetic energy per atom was 0.0517 eV. Which is closest to the temperature of the system obtained from the equipartition theorem? Take the Boltzmann constant as k = 8.617×10⁻⁵ eV/K.
  3. In a Monte Carlo calculation by the Metropolis method, a trial move of an atom raises the energy of the system by 0.10 eV. At a temperature of 1000 K, which is closest to the probability of accepting this move? Take k = 8.617×10⁻⁵ eV/K.
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  5. Which statement about the CALPHAD method is correct?